What is the best physical way to separate a mixture that has two different phases of matter? chromatography precipitation distillation filtration?

The answer is filtration. This is the best method because it is fast and cheap. It separates the different matter based on size of particles (since matter in different phases have different degrees of compaction of their atoms). The filter has a particular pore size that excludes the molecules of the solid since they are more compact as opposed to that of liquids of gases that are able to pass through since they are well dispersed.